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HARRISBURG, Pa. (AP) - Republican governors running for re-election next year are looking to capitalize on distaste for Washington gridlock and President Barack Obama's dropping public approval amid the bumpy rollout of his signature health care law - and Democratic challengers may need to respond with a popular cause.

A minimum wage increase could be the answer.

Democrats vying to challenge a slew of Republican governors, particularly those seeking re-election in states that Obama won last year, are talking up an increase as their campaigns get off the ground 11 months before the election.

Polls say it's publicly popular, it revives the message of economic inequality that Obama wielded effectively last year, and it comes wrapped in a broader jobs and economic message that touches on the top priority of many voting Americans.

In Pennsylvania, championing a minimum wage increase is already popular among the big field of Democrats vying to challenge the re-election bid of Gov. Tom Corbett.

Now, Katie McGinty, a onetime environmental policy adviser to the Clinton White House and Corbett's Democratic predecessor, is distinguishing herself by telling audiences and potential donors that she was the first Democrat in the Pennsylvania field to make it an issue.

"This is core for me," McGinty said. "I think it is fundamentally true across the centuries that one of the things that can really bring a nation down is the increasing chasm in terms of income."

All of those governors won a first term in the national Republican sweep of 2010, and most have had strong Republican representation in their legislatures to support them.

But LePage was tasked with facing a Democrat-controlled legislature, and in July he vetoed a bill to incrementally raise the state's minimum wage.

For his likely Democratic challenger, U.S. Rep. Mike Michaud, increasing the minimum wage is an issue the onetime paper mill worker from northern Maine discusses often, said campaign adviser David Farmer.

"He is closely aligned with working- and middle-class families," Farmer said. "He's not a millionaire."

Still, it would not be unheard of for a Republican to advocate a minimum wage increase. New Jersey Gov. Chris Christie, who leads the Washington, D.C.-based Republican Governors Association, and New Mexico's Martinez each vetoed their legislature's minimum wage bill, but not without making a counteroffer of a more modest increase.

Republican governors are focused on lightening tax and regulatory burdens for businesses to improve wages, said Jon Thompson, a spokesman for the Republican Governors Association. But he also seemed to acknowledge the occasional political necessity for Republicans to embrace a minimum wage increase.

"It's complicated because there are some states that a minimum wage increase could be more helpful and useful than other states," Thompson said in an email.

For Democrats, campaign advisers and strategists say there's no mandate from national party leaders to wield the issue as a weapon next year. But there's no denying it's popular and salient to the political battlefield, said Danny Kanner, spokesman for the Democratic Governors Association.

"The defining issue in every single one of these races is who is fighting for the middle class," he said.

Democrats are pairing their advocacy of a minimum wage increase with criticism of cuts to corporate tax rates, public pensions or education aid that Republican governors pushed through. They also contend that it'll revive the economy by flushing more money into the hands of consumers who spend it and reduce reliance on food stamps or other government programs for the poor.

If vulnerable Republicans aren't budging on the issue, neither are the big-business groups that tend to back them. The U.S. Chamber of Commerce warns that small employers will have the hardest time absorbing higher labor costs, while the National Federation of Independent Business warned of job losses.

"We're not going to waver," said NFIB spokeswoman Jean Card. "It's the kind of thing that sounds good, but rarely are polling questions backed up with the kind of economic downside that's inevitable."

For Democrats, Obama got the ball rolling on the issue by calling for an increase in his February budget speech, and union-organized demonstrations in front of profitable mega-chains such as Wal-Mart and McDonald's have kept it in the public eye.

And it's not only a popular issue with the labor unions that often provide money and volunteers to help power Democrats' campaigns - the public warmly embraces it, too.

An NBC News/Wall Street Journal survey this month found that more than six in 10 voting-age adults said they would support an increase of the federal minimum wage from $7.25, where it was last raised in 2009, to $10.10 an hour. Support to raise it to $12.50 fell to about four in 10 and fewer than three in 10 supported an increase to $15 an hour. A CBS News poll in November found that just one in four would like the federal minimum wage to remain at $7.25.

Some Democrats may nevertheless approach the issue with caution.

Mary Burke, who is expected to win the Democratic nomination to challenge Wisconsin's Walker, said she supports legislation there to increase the minimum wage by a relatively modest 35 cents an hour to $7.60.

Beyond that, the former state commerce secretary and daughter of Trek Bicycle's founder said a gradual and fair increase in the minimum wage could avoid economic harm. While she wasn't prepared to say what that is, the subject will be prominent in her campaign, Burke said.

"This race is going to be about jobs and people being able to support themselves," Burke said, "and that is an important way we can help more people move toward economic independence."